I am running a series of CFAs with censored variables and would like to use the MLR estimator due to missing data. I am not getting regular fit indices (chi-square, CFI, TLI, RMSEA) when I use this estimator. Do these need to be requested?
Maximum-likelihood estimation with censored variables does not have means, variances and covariances as sufficient statistics, but instead raw data, and therefore does not do the usual model test of fit. If you want a test of the fit to the covariance matrix you can use WLSMV. You can also use MLR and create your own unrestricted covariance matrix model in Mplus to test against, that is do a second run, and then compute chi-square as 2 times the log likelihood difference.
I spoke too quickly in my last sentence above. To do what I suggested one must allow a factor behind each censored variable which will lead to too many dimensions of integration with MLR.
Instead, you can either use WLSMV for such testing and hope that the missing data handling in WLSMV is sufficient. Or, better still, use MLR and work with likelihood-ratio chi-square testing of nested neighboring models to see if specific restrictions in your model are well fitting or not.
Dr. Muthen. Thank you for your prompt response. I had originally used the censored with WLSMV, but after reading more about estimators it seemed that MLR might be more appropriate. I appreciate your suggestions.